Dendroclimatic Analyses

You now have the climate variables. What’s the You now have the climate variables. What’s the next step?next step?

• Statistical analyses to select the ONE climate variable to Statistical analyses to select the ONE climate variable to eventually reconstruct.eventually reconstruct.

• We must first carefully analyze the climate/tree growth We must first carefully analyze the climate/tree growth relationshiprelationship

• Response function analysis:Response function analysis:• biological model of tree growth/climate relationshipbiological model of tree growth/climate relationship• developed by Hal Fritts in early 1970sdeveloped by Hal Fritts in early 1970s• uses the final tree-ring chronology developed after uses the final tree-ring chronology developed after

standardizationstandardization• uses monthly temperature and precipitationuses monthly temperature and precipitation• uses months from the previous year as well (why?)uses months from the previous year as well (why?)

Response function analysis:Response function analysis:• uses principal components (PC) multiple regressionuses principal components (PC) multiple regression• PC analysis removes effects of interdependence PC analysis removes effects of interdependence

among climate variablesamong climate variables• more recent software (PRECON) also uses more recent software (PRECON) also uses

bootstrapping to calculate confidence intervalsbootstrapping to calculate confidence intervals• notice r-squared values due to climate and prior notice r-squared values due to climate and prior

growthgrowth• interpret the diagram. Look for bumps, humps, dips, interpret the diagram. Look for bumps, humps, dips,

and dumps.and dumps.• Bump = single positive monthly variableBump = single positive monthly variable• Hump = two or more consecutive positive Hump = two or more consecutive positive

monthly variablesmonthly variables• Dip = single negative monthly variableDip = single negative monthly variable• Dump = two or more consecutive negative Dump = two or more consecutive negative

monthly variablesmonthly variables

Response function analysis:Response function analysis:

Response Function AnalysisResponse Function Analysis

Correlation analysisCorrelation analysis• Correlation analysis complements results from

response function analysis.• RFA primarily concerned with temp and precip.

Correlation analysis can be done on ALL climate variables (PDSI, ENSO, PDO, etc.)

• Correlation analysis best done with stats packages (SAS, Systat) or PRECON.

• Range of values = -1.0 < r < +1.0• Associated with each r-value is its p-value which

tests for statistical significance.• In general, we want p-values less than 0.05, or p <

0.05.• As in response function analysis, we also analyze

months from the previous growing season (why?).• As in response function analysis, we look for

groupings of monthly variables to indicate seasonal response by trees.

Correlation analysisCorrelation analysis

Graphical output from PRECON. Any value above +0.2 or below -0.2 is significant.

Positive!

Negative!

Note how response function analysis (top) and Note how response function analysis (top) and correlation analysis (bottom) are complementary correlation analysis (bottom) are complementary (but different).(but different).

Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations

lmayt ljunt ljult laugt lsept loctt lnovt

-0.08019 -0.03131 -0.34233 -0.16914 -0.29516 -0.09849 -0.02712 0.4941 0.7897 0.0023 0.1414 0.0096 0.4071 0.8173 75 75 77 77 76 73 75

Correlation analysisCorrelation analysis

• R-values also known as Pearson correlation R-values also known as Pearson correlation coefficientscoefficients

• SAS output below: r-value (top), p-value (middle), n SAS output below: r-value (top), p-value (middle), n size (bottom)size (bottom)

• How do you interpret negative correlations?How do you interpret negative correlations?

Pearson Correlation Coefficients Prob > |r| under H0: Rho=0 Number of Observations

jult augt sept octt novt dect

-0.41391 -0.18258 -0.21850 -0.08422 -0.02171 -0.13367 0.0002 0.1120 0.0579 0.4756 0.8534 0.2562 77 77 76 74 75 74

Correlation analysisCorrelation analysis

Stepwise multiple regression analysisStepwise multiple regression analysis• Another complementary techniqueAnother complementary technique

Why do the two series diverge here?

Climate ReconstructionClimate Reconstruction

• You’ve chosen your ONE climate variable to reconstruct You’ve chosen your ONE climate variable to reconstruct based on these analyses.based on these analyses.

• Use ordinary least squares regression techniques, which Use ordinary least squares regression techniques, which says:says:

• Tree growth is a function of climate, but we want to Tree growth is a function of climate, but we want to reconstruct climate.reconstruct climate.

• Instead, we state climate is a function of tree growth.Instead, we state climate is a function of tree growth.• x-values are the predictor variable = tree-ring x-values are the predictor variable = tree-ring

chronologychronology• y-values are the predictand variable = climate variabley-values are the predictand variable = climate variable

^• y = ax + b + ey = ax + b + e is the form of the regression lineis the form of the regression line• In many older studies, it was common to conduct a In many older studies, it was common to conduct a

regression over a calibration period (e.g. 1951-1990), regression over a calibration period (e.g. 1951-1990), and verify this equation against data in a verification and verify this equation against data in a verification period (e.g. 1910-1949) to ensure the robustness of the period (e.g. 1910-1949) to ensure the robustness of the predicted values.predicted values.

• In SAS:In SAS:• proc reg; model jult = std;proc reg; model jult = std;• where “jult” = July temperature being where “jult” = July temperature being

reconstructed, andreconstructed, and• ““std” = the tree-ring (standard) chronologystd” = the tree-ring (standard) chronology

• In the regression output, you will be given the regression In the regression output, you will be given the regression coefficient (a) and the constant (b).coefficient (a) and the constant (b).

• To generate predicted climate data before the To generate predicted climate data before the calibration period, plug these two values into an calibration period, plug these two values into an equation to predict July temperature.equation to predict July temperature.

• Do this for the full length of the tree-ring record for each Do this for the full length of the tree-ring record for each year.year.• predict = (9.59154*std) + 32.96236;predict = (9.59154*std) + 32.96236;• where “predict” is predicted July temperature and where “predict” is predicted July temperature and

“std” = the tree-ring data.“std” = the tree-ring data.

Climate ReconstructionClimate Reconstruction

Reconstructed Bemidji Feb-May Mean Monthly Max TempClimate ReconstructionClimate Reconstruction

Reconstructed Water Year Rainfall, New Mexico

Reconstructed Nov-Apr average temp, Tasmania

Reconstructed Blue River Annual Streamflow, Colorado

Reconstructed Temperatures from Multiple Proxies, the famous “Hockey Stick” graph